BGE: Can a rigged rigid body interact with BGE physics?
An armature rigged mesh cannot interact with other rigidbody objects, as the mesh deformation by the bones are not sent to the physics engine. (They are actually done on the GPU as of Blender 2.71 [source])

Your only option is to parent a bunch of collision proxies to the armature and use those instead of the actual rigged mesh, like this.